1. Field of the present invention
The present invention relates to a Hadamard transform coding/decoding device for image signals using two-dimensional Hadamard transform.
2. Description of the Related Art
A Hadamard transform coding technique for image signals is described in "DIGITAL SIGNAL PROCESSING OF IMAGES--enlarged edition--"by Takahiko Fukinuke, pp181-193 (issued on Jan. 27, 1992 by Nikkan Kogyo Shinbunsha), and "MULTIDIMENSIONAL SIGNAL PROCESSING OF TV SIGNALS" by Takahiko Fukinuke, pp247-250 (issued on Nov. 15, 1988, first edition by Nikkan Kogyo Shinbunsha).
Now, representing image data of 8 rows and 8 columns (8.times.8) by a matrix X=[x(i,j)], (i=0,1, . . . , 7; j=0,1, . . . , 7), a matrix Y of the transform coefficients of the two-dimensional (8.times.8)-th order Hadamard transform (=[y(h,v)]) is calculated according to Y=HXH/8 (h=0,1, . . . , 7; v=0,1, . . . ,7). Here, H is represented by the following matrix: ##EQU1## Here, the Hadamard inverse-transform is represented by X=HYH/8.
Furthermore, with respect to the coding based on a two-dimensional (8.times.8)-th order discrete cosine transform (DCT), the ITU-T recommendation T.81 or ISO/IEC standard 10918-1 describes a manner of predicting AC coefficients of a block concerned on the basis of the DC coefficients of the block concerned and adjacent blocks to reduce a coding amount. According to this coding amount reducing manner, the image waveform of each block is approximated by the following equation 2, and the transform coefficient of the approximated waveform is set as a prediction value. EQU f(i,j)=A1i.sup.2 j.sup.2 +A2i.sup.2 j+A3ij.sup.2 +A4i.sup.2 +A5ij+A6j.sup.2 +A7i+A8j+A9 (2)
The constants A1, A2, . . . , A9 of the above equation (2) are set so that the DC coefficient of the approximate waveform in the block concerned and eight blocks adjacent to the block concerned is coincident with the actual DC coefficient. In the ITU-T recommendation T.81 is provided a prediction equation for five AC coefficients in a low area. That is, representing the DC coefficient of the block concerned by Dc and representing the DC coefficients of the adjacent eight blocks by Dnw (northwest) at left-and-upper side, Dn (north) at upper side, Dne (northeast) at right-and-upper side, Dw (west) at left side, De (east) at right side, Dsw (southwest) at left-and-lower side, Ds (south) at lower side and Dse (southeast) at right-and-lower side, the prediction value of a transform coefficient of first-order in the horizontal direction and zero-order in the vertical direction is set to 36 (Dw-De)/256, the prediction value of a transform coefficient of second-order in the horizontal direction and zero-order in the vertical direction is set to 9(Dw-2Dc+De)/256, the prediction value of a transform coefficient of zero-order in the horizontal direction and first-order in the vertical direction is set to 36 (Dn-Ds)/256, the prediction value of a transform coefficient of first-order in the horizontal direction and first-order in the vertical direction is set to 5(Dnw-Dne-Dsw+Dse)/256, and the prediction value of a transform coefficient of zero-order in the horizonal direction and second-order in the vertical direction is set to 9(Dn-2Dc+Ds)/256. The prediction values as described above are optimized by the DCT (discrete cosine transform).
However, since the Hadamard transform based on the prior art as described above is considered to have no perfect reversibility in the case of DCT, it is not effective to directly apply the prediction equation of the DCT to the Hadamard transform, and it is required to optimize the prediction equation for the Hadamard transform.
Japanese Post-examined publication (Kokai) No. Hei-1-33992 "ORTHOGONAL TRANSFORM CODING DEVICE" and Japanese Laid-open Patent Application No. Hei-3-289282 "HIGH-EFFICIENT CODING DEVICE FOR IMAGE DATA" are known as prior art which belong to the related technical field as the present invention. However, since these prior art references use the same order transform coefficient for the prediction of image signals, they are different from the present invention.